“We are beyond devastated,” Miller said in an Instagram post that showed several photos of the chubby-cheeked toddler.

In a video, Emmy, as she was known, was being kissed on the cheek by her mother Morgan, a professional beach volleyball player, as she repeatedly said “Hi Dada”.

“Never in a million years did we think we would experience a pain like this,” Miller said in the post.

“Her love, her light, her spirit will never be forgotten. Our little girl loved life and lived it to its fullest every day.”

Paramedics were called to a home in the upscale enclave of Coto de Caza just before 6:30pm on Saturday (local time).

They tried unsuccessfully to resuscitate the girl and rushed her to hospital.

“They had no pulses the whole way,” Captain Tony Bommarito of the Orange County Fire Authority said. “It didn’t end well.”

A spokewoman for the Orange County Sheriff’s Department said the death was under investigation.

The US Ski and Snowboard Team tweeted its condolences to Miller and his family.

Miller, 40, is the most decorated male US skier with 33 World Cup wins, two overall titles, four world championships and six Olympic medals, including gold at the 2010 Vancouver Games in the super-combined.